As a political methodologist (the part of The Discipline™ that specializes in probability and statistics), I probably ought to be more interested in baseball than I am. After all, baseball is the most stats-intensive sport in the world by far, largely because it consists of a large number of repetitions of people doing basically the same things—hitting, fielding, and pitching—over and over again, and large numbers of repetitions mean you can make good generalizations from the data. Of course, early in the season, your generalizations can be pretty bad.

David Pinto at Baseball Musings looks at the example of the Kansas City Royals, who are the only remaining undefeated team in the majors, with eight wins so far, but who have been predicted to only win 66 of 162 (or 40.74% of their games). It turns out that there’s an 11.1% chance that a team winning 66 games would have an eight-game winning streak during its season, which most statisticians would attribute to being within the realm of random chance (generally we like 5% as a cutoff).

For fun, extending it to a 9-win streak reduces it to 4.65% (below the 5% level), or just about 1 in 22. At that point, I’d be pretty confident that the Royals will win more than 66, since in 21 of 22 seasons a team that would eventually only win 66 would never have a 9-game winning streak.

For R geeks: evaluate either 1-dbinom(0, 155, dbinom(8, 8, 66/162)) or sum(dbinom(1:155, 155, dbinom(8, 8, 66/162))), depending on your mood. You should get 0.1110256. Change the 155 to 154 and the 8s to 9s to evaluate the 9-win streak hypothesis.

The Royals’ winning streak did end at nine games. Also, David Pinto talks some more about confidence levels (and generously links here) in this post; note that if the prediction had been 67 games, the probability of a 9-win streak would edge above the 5% confidence level (to 5.31%), which indicates both the arbitrariness of a chosen confidence level and that the Royals could still stink up the joint.

Jed Roberts correctly points out that David and I make an invalid independence assumption in the streak calculations that potentially overestimates the probability of a given streak occurring during a season. David also carries a lengthy comment from Michael Weddell on the significance of the Royals’ streak.